A native of Yakutsk, Izmaylov attended a navigation school in Okhotsk with Dmitry Bocharov, who became his lifelong business companion. In 1771, both were caught up in the Benevsky mutiny on Bolsheretsky island in Kamchatka. Izmaylov attempted to break away from the mutineers but, after being flogged, was marooned on the isle of Simushir, one of the uninhabited Kuril Islands. For a year he subsisted on "scallops, grass, and roots" before being rescued by yasak gatherers. He was tried in Irkutsk on charges of mutiny, but was eventually cleared in 1774.

In 1775, Izmaylov assumed command of the boat St. Paul and set to work mapping the shores of the Aleutian Islands. On October 1778, while visiting Unalaska, he made the acquaintance of Captain James Cook who presented him a sword and a Mercator map in exchange for a letter of introduction to the Kamchatka authorities. He also handed over to Izmaylov a recently drawn map of the western coast of North America, which was to be delivered by the Russians to the British Admiralty.

In 1783-1785, Izmaylov and Grigory Shelikhov made their historic voyage from Okhotsk to Kodiak Island, where they founded the first Russian settlement in America. In 1789, Izmaylov became the first to explore and map the Kenai Peninsula. Three years later, he took up employment under Alexander Baranov, helping him withstand a sea attack by the Tlingit.

Having wintered in Unalaska, Izmaylov visited Saint Paul Island, where he discovered the crew of a Russian ship that had been missing since 1791. He brought them back to Okhotsk in June 1794. He is mentioned for the last time in 1795, when he accompanied to Alaska a group of Orthodox missionaries under Father Joasaph.